3. Neil Bohr postulated
Electron does not radiate energy as it moves in a particular orbit.
Electron can move from one orbit to another absorbing or radiating
energy.
Centrifugal force in which electron orbits is equal to electrostatic force,
thus electron remains in orbit.
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4. Calculating Bohr radius
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Electron to remain in orbit
𝑪𝒆𝒕𝒓𝒊𝒇𝒖𝒈𝒂𝒍 𝒇𝒐𝒓𝒄𝒆
= 𝑬𝒍𝒆𝒄𝒕𝒓𝒐𝒔𝒕𝒂𝒕𝒊𝒄 𝒇𝒐𝒓𝒄𝒆
𝑚𝑣2
𝑟
=
𝑍𝑒2
4𝜋𝜀°𝑟2 …………..1
Where,
r is radius of atom, mass of electron m =
9.1091 X 10-31 Kg; charge on electron e =
1.60210 X 10-19 C; vacuum permittivity
of vacuum εo = 8.854185 X 10-12J-1m-1C2
r
5. Calculating Bohr radius
According to Plank ‘Energy is discrete’: only certain energy levels are
possible which integral multiple of h/2𝜋 ( of n a whole number 0, 1, 2, 3…)
Plank constant h = 6.6262 X10-34Js
𝐴𝑛𝑔𝑢𝑙𝑎𝑟 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 = 𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑠𝑡𝑎𝑡𝑖𝑐 𝑓𝑜𝑟𝑐𝑒
𝑚𝑣𝑟 =
𝑛ℎ
2𝜋
………………..2
From 1 and 2
𝑟 =
𝑛2ℎ2ε°
𝜋𝑍𝑚𝑒2
For Hydrogen, Z = 1, than for
n=1; r = 1 X 0.0529 nm
n=2; r = 22 X 0.0529 nm
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6. Energy of orbit and energy of
electronic transition
For energy we can consider equation 1
𝐸 = −
1
2
𝑚𝑣2
= −
𝑍2𝑒4𝑚
8 𝑛2ℎ2ε°
2………………..3
Difference in energy (ΔE) of two orbits
𝐸2 − 𝐸1 = −
𝑍2
𝑒4
𝑚
8𝑛2
2ℎ2ε°
2 − (−
𝑍2
𝑒4
𝑚
8𝑛1
2ℎ2ε°
2)
ΔE =
𝑍2𝑒4𝑚
8ℎ2ε°
2 (
1
𝑛1
2 −
1
𝑛2
2) ………………..4
7. Energy of orbit and energy of
electronic transition
𝐸 = ℎ𝑣 = ℎṽ𝐶
ṽ = 𝑤𝑎𝑣𝑒𝑛𝑢𝑚𝑏𝑒𝑟
Then,
ṽ =
𝑍2𝑒4𝑚
8ℎ3ε°
2𝐶
(
1
𝑛1
2 −
1
𝑛2
2)
ṽ = 𝑅 (
1
𝑛1
2 −
1
𝑛2
2)
R= Rydberg constant =1.0973 X 107 m-1
8. Bohr orbit of hydrogen atom and
spectral series
Series name n1 n2 ʎ nm Electromagn
etic radiation
Lyman 1 2,3,4,5… 91.2-121.6 UV
Balmer 2 3,4,5,6… 383.5-656.2 Visible
Paschen 3 4,5,6,7… 954.6-
1875.0
Infrared
Brackett 4 5,6,7,8… 2630-4050 Infrared
Pfund 5 6,….. 7400 infrared
9. Limitations
• Spectral lines is a collection of several lines very
close together.
• does not spectral series for the atoms having a
more number of electrons.
• Bohr theory does not explain the use of the
principle of quantization of energy
• Bohr assumes electrons are at a fixed point
• No justification of the Zeeman effect or Stark
effect.
10. Bohr's Theory
• Why electron does not slow down as it moves in orbit?
• Why circular path it follows?
• Why electron does not collide with nucleus as electron
is negative and nucleus positive.
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